Bounds for the Euclidean minima of function fields

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We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

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This work generalizes the one-step model previously developed on fcc-bcc martensitic transformations to the larger family of phase transitions in the fcc-bcc-hcp system. The angular distortive matrices are calculated for the bcc-fcc, bcc-hcp and fcc-hcp tr ...

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

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In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields define ...

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

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The performance of HTS devices is strongly influenced by local values of the current/field distributions. In this paper, we investigate the influence of the magnetic field and of the geometrical configuration on the loss behaviour of a 200kVA FCL prototype ...

Bounds for the Euclidean minima of function fields

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